At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at least 1 prize?
| # of Prizes | 0 | 1 | 2 | 3 |
| :---------- | :--- | :---- | :---- | :---- |
| Probability | ? | 0.41 | 0.33 | 0.09 |
Answer (1)
Calculate the probability of winning 0 prizes: P ( 0 ) = 1 − 0.41 − 0.33 − 0.09 = 0.17 .
Calculate the probability of winning at least 1 prize: P ( at least 1 ) = 1 − P ( 0 ) = 1 − 0.17 = 0.83 .
The probability that Kylee wins at least 1 prize is 0.83 .
Explanation
Understand the problem We are given a table with the probabilities of Kylee winning 1, 2, or 3 prizes at a carnival game. We want to find the probability that she wins at least 1 prize. This is the complement of the probability that she wins 0 prizes.
Calculate the probability of winning 0 prizes First, we need to find the probability of winning 0 prizes. We know that the sum of the probabilities of winning 0, 1, 2, or 3 prizes must equal 1. Therefore, we can calculate the probability of winning 0 prizes as follows: P ( 0 ) = 1 − P ( 1 ) − P ( 2 ) − P ( 3 ) P ( 0 ) = 1 − 0.41 − 0.33 − 0.09 P ( 0 ) = 1 − 0.83 P ( 0 ) = 0.17
Calculate the probability of winning at least 1 prize Now that we have the probability of winning 0 prizes, we can find the probability of winning at least 1 prize. This is the complement of winning 0 prizes: P ( at least 1 ) = 1 − P ( 0 ) P ( at least 1 ) = 1 − 0.17 P ( at least 1 ) = 0.83
State the final answer Therefore, the probability that Kylee wins at least 1 prize is 0.83.
Examples
Imagine you're at a school fair where you can win prizes by throwing rings onto bottles. If you know the chance of winning nothing is 17%, then the chance of winning at least one prize is 83%. This helps you decide if it's worth playing the game!
